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S- parameters in a Two Port Network Purpose and Discussion The purpose of this simulation is to demonstrate the characteristics of scattering parameters utilizing Multisim’s Network Analyzer. When subatomic particles are accelerated, collisions with atoms result, and scattering parameters are generated. Though their name was derived through particle physics, a portion of the theory of scattering parameters is used in areas such as transmission line theory and microwave active devices. In transmission line theory, forward scattering corresponds to transmission and backward scattering corresponds to reflection. Interchanging the source and load produces reverse coefficients S22 and S12. Transmission and reflection coefficients are denoted by S21 and S11. Knowledge of the values of s-parameters in describing active devices means that circuits may be designed around the device with little or no understanding of the internal device operation. The reflection or scattering of electromagnetic waves is fundamental to the analysis and design of microwave circuitry. In this experiment, scattering parameters will be calculated using Multisim’s Network Analyzer with a simple two port network. A- Resistive Two Port Network For the network shown, 1- Calculate the s- parameters according to the equations listed below and put the results I nthe provided table. Necessary Equations: Using ABC matrices: series: � = $ 1 � 0 1 (, R here = 80 Ohms Parallel: � = * 1 0 1/� 1, R = 40 ohms Parallel: : � = * 1 0 1/� 1, R = 50 ohms The line impedance is Zo = 50 ohms abc is the product of the matrices a*b*c m order The resulting matrix is now a 2 X 2 matrix. ��� = � ∗ � ∗ � = $ � � � �( When you multiply a*b*c you obtain a matrix of four elements (2X2) Let us call the elements as A, B,C, and D as shown in the matrix above. The S-parameters are calculated as follows: Note, A,B,C, and D are the elements of the resulting matrix abc. Show Calculations �44 = � + � �� − ��� − � � + � �� + ��� + � �49 = 2(�� − ��) � + � �� + ��� + � �94 = 2 � + � �� + ��� + � �99 = −� + � �� − ��� + � � + � �� + ��� + � The results are: Scatter Parameter Value S11 S12 S21 S22 Place the resulting S parameters in a matrix format S = * �44 �49 �94 �99 , 2- Using Multisim, simulate the circuit. Verify the correctness of your calcualtions. Insert a snap shot of the Multisim result Ensure to set the network Analyzer as shown (Measurement, S-Parameters, Polar) 2- Using Multisim only, replace the 80 Ohm in the circuit by a 15uH inductor and change the frequency to 144.544MHz. Display your results.

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